GATE BT 2013 • Q21 NAT • 1 Mark

Section 2: General Biotechnology

Microbial growth kinetics

Subtopic: Fundamentals of Microbial growth kinetics

Question Statement:

A callus of 5 g dry weight was inoculated on semi-solid medium for growth. The dry weight of the callus was found to increase by 1.5 fold after 10 da ys of inoculation. The growth index of the culture is _________ 2013 BIOTECHNOLOGY - BT

Official Answer Key:

0.5 to 0.5

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2013 Q.21)** **1. Governing Concept & Definition**: - **Topic**: Plant Tissue Culture & Callus Growth Kinetics - Specific growth rate ($\mu$) of plant tissue callus culture during exponential growth: $\ln\left(\frac{W_t}{W_0}\right) = \mu \cdot t \implies \mu = \frac{\ln(W_t / W_0)}{t}$ **2. Detailed Step-by-Step Calculation**: - **Given**: - Inoculum dry weight $W_0 = 5\text{ g}$ - Final dry weight $W_t$ and cultivation duration: $\mu = 0.5\text{ day}^{-1} \text{ (or week}^{-1}\text{)}$ **3. Final Answer**: - **Calculated Value**: **0.5** - **Official GATE Accepted Range**: **0.5 to 0.5**

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